An engineering firm is interested in investigating whether the variability in the cost of small projects (defined as projects under $10 million) can be accounted for, in part, by differences in the number of direct engineering consulting hours billed. A random sample of 24 small projects was randomly selected from small projects performed over the past two years. The number of engineering consulting hours billed for each project, along with the project€™s cost, was recorded. The results are shown below:

a. Develop a simple linear regression model to explain the variation in total project cost based on the number of billed consulting hours.
b. Construct and interpret a 95% confidence interval estimate for the regression slope coefficient.
c. Provide a 95% confidence interval for the average value of y when xp = 3,500.
d. Provide a 95% prediction interval for total project cost for a particular project with 3,500 billed consulting hours.

Billed Consulting Total Project Project Hours Cost 3932 3097 2972 3994 4906 5147 4003 4279 3158 4123 2566 3253 3888 3177 3938 3135 5142 5091 4301 2914 3890 2869 3683 4217 4.323.826 S3,750,964 S3.579,570 S5.053.149 S5.528,308 S5,631,967 S5,257,756 S5,681909 S4,133.012 S4.596.329 S3.344.851 S3,868.200 $4,865,998 S4,042,509 S5,067,679 S4,111.731 S6,554,583 S6,042.445 S5,192,769 S3,581.835 S4.745.269 S3.353.559 S5,169,469 S5,147.689 3 10 12 13 15 16 17 19 20 23 24